>> In message <slrnh33j2b.4bu.pe...@box8.pjb.com.au>, Peter Billam wrote: >>> Are there any modules, packages, whatever, that will >>> measure the fractal dimensions of a dataset, e.g. a time-series ? > Lawrence D'Oliveiro wrote: >> I don't think any countable set, even a countably-infinite set, can >> have a fractal dimension. It's got to be uncountably infinite, and >> therefore uncomputable.
You need a lot of data-points to get a trustworthy answer. Of course edge-effects step in as you come up against the spacing betwen the points; you'd have to weed those out. On 2009-06-14, Steven D'Aprano <st...@removethis.cybersource.com.au> wrote: > Strictly speaking, there's not one definition of "fractal dimension", there > are a number of them. One of the more useful is the "Hausdorf dimension", They can be seen as special cases of Renyi's generalised entropy; the Hausdorf dimension (D0) is easy to compute because of the box-counting-algorithm: http://en.wikipedia.org/wiki/Box-counting_dimension Also easy to compute is the Correlation Dimension (D2): http://en.wikipedia.org/wiki/Correlation_dimension Between the two, but much slower, is the Information Dimension (D1) http://en.wikipedia.org/wiki/Information_dimension which most closely corresponds to physical entropy. Multifractals are very common in nature (like stock exchanges, if that counts as nature :-)) http://en.wikipedia.org/wiki/Multifractal_analysis but there you really need _huge_ datasets to get useful answers ... There have been lots of papers published (these are some refs I have: G. Meyer-Kress, "Application of dimension algorithms to experimental chaos," in "Directions in Chaos", Hao Bai-Lin ed., (World Scientific, Singapore, 1987) p. 122 S. Ellner, "Estmating attractor dimensions for limited data: a new method, with error estimates" Physi. Lettr. A 113,128 (1988) P. Grassberger, "Estimating the fractal dimensions and entropies of strange attractors", in "Chaos", A.V. Holden, ed. (Princeton University Press, 1986, Chap 14) G. Meyer-Kress, ed. "Dimensions and Entropies in Chaotic Systems - Quantification of Complex Behaviour", vol 32 of Springer series in Synergetics (Springer Verlag, Berlin, 1986) N.B. Abraham, J.P. Gollub and H.L. Swinney, "Testing nonlinear dynamics," Physica 11D, 252 (1984) ) but I haven't chased these up and I don't think they contain any working code. But the work has been done, so the code must be there still, on some computer somwhere... Regards, Peter -- Peter Billam www.pjb.com.au www.pjb.com.au/comp/contact.html -- http://mail.python.org/mailman/listinfo/python-list
